Mathematics teachers’ instructional strategies lack in-depth knowledge of algebraic systems and hold misconceptions about solving two algebraic equations simultaneously. This study aimed to gain an in-depth analysis of teachers’ knowledge and perceptions about the promotion of conceptual learning and effective teaching of algebraic equations. The main question was, ‘How do junior secondary school mathematics teachers manifest their pedagogical practices when teaching algebraic equations? This article reports on a qualitative, underpinned by the knowledge quartet model study, that sought to explore how junior secondary school teachers’ pedagogical practices manifested in the teaching of algebraic equations. Data were collected from observations, semi-structured interviews, and document analysis of two mathematics teachers purposely selected from two schools. The collected data were analysed using a statistical analysis software called Atlas-ti. (Version 8) and triangulated through thematic analysis. The study revealed that teachers’ choices of representations, examples, and tasks used did not expose learners to hands-on activities that promote understanding and making connections from the underlying algebraic equation concepts. The study proposed Penta-Knowledge Collaborative Planning and Reflective Teaching and Learning Models to enable teachers to collaborate with their peers from the planning stage to lesson delivery reflecting on good practices and strategies for teaching algebraic equations.

The skill to solve mathematical problems facilitates students to develop their basic skills to solve problems in daily life. This study analyzes students' problem-solving process with a reflective cognitive style in constructing probability problems using action, process, object, and schema theory (APOS). The explanatory method was used in this qualitative study. The participants were mathematics students at the Department of Mathematics, Universitas Negeri Semarang. The researchers collected the data with the cognitive style test using the Matching Familiar Figure Test (MFFT), used a valid problem-solving skill test, and the interview questions. The data analysis techniques used were processing and preparing the data for analysis, extensive reading of the data, coding all data, applying the coding process, describing the data, and interpreting the data. The results showed that (1) the problem-solving process of students with symbolic representation was characterized by the use of mathematical symbols to support the problem-solving process in the problem representation phase; (2) the problem-solving process of students with symbolic-visual representation was characterized by the use of symbols, notations, numbers, and visual representation in the form of diagrams in the problem representation phase.

Metacognitive, critical thinking and opinion expression are in high demand. This study aimed to investigate the effects of the blended project- based literacy that integrates school literacy movement strengthening character education (literasi berbasis proyek terintegrasi GLS dan PPK: Li-Pro-GP) learning model on students' metacognitive skills, critical thinking, and opinion expression. A post-test experimental design was used to answer the research question. The study was conducted from August to October 2021 at Government Junior High School 23 Malang. Seventh-grade students were selected as research participants. The participants included 30 students from class VII-2. The research instrument was five essay questions to measure critical thinking skills. Material and assessment experts validated the essay questions developed by the researcher. The items that were declared valid were tested for validity. The result showed five valid items with high reliability of .670. Metacognitive skills were measured using the Metacognition Awareness Instrument (MAI), which consists of 40 items. The questions declared valid were tested for validity with a very high reliability of .953 for 37 items, and only three items were invalid. The ability to express an opinion was measured with an observation questionnaire validated by experts with a valid instrument score. Data analysis was performed by path analysis using the SmartPLS software. The results showed that the Li-Pro-GP blended learning model significantly strengthened students' metacognitive skills, critical thinking, and opinion formation.

The aim of this work is to characterise the understanding that students in compulsory secondary education (14-16 years old) have of number sequences in graphical representations. The learning of numerical sequences is one of the first mathematical concepts to be developed in an infinite context. This study adopts the focus of semiotic representations as its theoretical framework. The participants consisted of 105 students and a qualitative methodology was used. The data collection instruments were a questionnaire and a semi-structured interview. The results allowed for three student profiles regarding number sequences in graphical representations to be identified. These profiles may facilitate a possible progression in the learning of number sequences for students in compulsory secondary education to be considered. Therefore, the results presented in this study can provide information about the learning hypotheses of mathematical tasks related to numerical sequences and can help in the design of such tasks.

This study aims to investigate lecturers' needs for academic writing learning materials and determine their prototypes. This study is qualitative research in the form of an exploratory case study. The research instruments were semi-open-ended questionnaires and unstructured and open-ended interview guides. The data were analyzed using content analysis. The results show that the developed learning material for academic writing skills contains seven needs for lecturers in the Department of Indonesian Language and Literature. Four of them have not been found by previous researchers. The results from this study provide new knowledge and contribution to the literature about the need to prototype the learning materials. The lecturers or other researchers can use these seven needs in prototyping learning materials for academic writing skills, such as the needs of learning materials, their forms, presentation system, language use, evaluation form, main menu design, and the way of creating learning materials.

Teaching a subject in a vocational high school (VHS) requires specialized instructional design strategies. Recently, instructional VHS used a computer-based platform to teach theory and practice. The computer will assist teachers in creating instructional media. This study aims to design augmented reality-based virtual laboratory media for electro-pneumatic practicum learning in order to ease teachers and students to learn the pneumatic practice. It is specially designed for practical learning purposes. The method used in this research is research and development. The assessment results from Instructional design experts 4.5, material experts 4.5, media experts 4.4, and language experts 4.8. Based on the assessment of experts, this augmented reality-based virtual laboratory media is feasible to use. Next, the results of this study are a prototype of students' pneumatic practice tools installed on mobile phones consisting of eight worksheets. In the designed augmented reality media, 1) 3-dimensional pneumatics can be rotated in all directions so that students understand. 2) Pneumatic job sheet, where on the augmented reality media designed for the simulation circuit, there is an explanation of the components and how they work, and a simulation through markers.

This study analyzes the narrated reflection of the students in relation to their learning, based on the perceptions that emerge from their experience in the development of the project. Participants were 53 fourth year Pedagogy in Physical Education students, with an average age of 24.3, who were divided into 13 groups. A qualitative study that used the narrated reflection of the students in relation to learning, based on a driving question. In order to help guide the students’ work, and to collect the perceptions they experienced during their participation, the following four components were integrated into the development of the project and included in the final product: a) historical and heritage sites, b) technology used to measure energy expenditure, c) type of active commuting, d) reflection on what was learned. The students designed 13 routes of active commuting through the city, which included different cultural, heritage and historical landmarks. The students analyzed the learning experience, highlighting the importance of knowing and caring for the heritage of the different cities around which they traveled. PBL can be a didactic alternative in initial Physical Education teacher training to achieve learning by linking subject content with the motivations and interests of the students.

During the pandemic, online classes were held around the world, which facilitated access to observe teaching practices. This is a relevant experience, since there are few reflective instances in schools, even though public education policy emphasizes reflective practice in the professional development of teachers. In this regard, the observation of videos shows high reflective potential, helping to problematize and analyze teaching. This research sought to describe the functions and experience of classroom video observation with a reflective approach of teachers from four educational schools in the city of Concepción, Chile. The approach was interpretative, an instrumental case study design, with nine participants, selected by a maximum variation sampling and safeguarding ethical criteria. In-depth interviews were conducted and subjected to content analysis. The results showed three functions of the video observation, one instrumental and two others of reflective approach. In addition, the video observation was recognized as a reflective experience that facilitates the reconsidering of teaching performance, renewing practices, and developing reflective habits; also, facilitating and hindering elements were found in the video observation. It is concluded that the functions and experience of video observation could improve and professionalize teaching, based on the awareness and understanding of practice.

The teaching of speaking in English as a foreign language (EFL) classes in the Province of Aceh did not rely on the suggested techniques and methods. This teacher-designed technique, which was mainly textbook-based, has left an unpleasant learning experience among students. Therefore, we conducted a quantitative research study to experiment with how students responded to contextual teaching and learning (CTL) to see the effect of transitioning from a teacher-established method to a systematically planned learning approach and compare how students progressed over time. The experiment was carried out by teachers who had received assistance in preparing the lesson and practicing the lesson plan. The six-meeting experiment was conducted in 11 small classes, with a total sample of 132 students. The student improvement after the first four meetings (cycle 1) was compared using inferential statistical analyses with that after eight meetings (cycle 2). The results show that the student’s achievement significantly improved in the first cycle and continued to improve, although at a lower rate, in the second cycle. This result suggests that CTL can be used to transition from a traditional teaching method to a more established method in EFL teaching. Therefore, teachers need help planning their teaching and practicing how to implement the teaching plan accurately.

21st-century learning requires teachers and students to integrate literacy skills, scientific literacy, mathematics, reading, writing, and technology in the learning process. Students must have initiative, discipline, responsibility, confidence, motivation for independent learning, and the ability to think critically about the problems presented. This study aims to determine students' autonomous knowledge and critical thinking abilities (CTA) using mobile learning technology (MLT). This research is a quantitative study involving 83 students from four junior high schools in the city of Mataram. The data collection for independent learning and students' CTA was carried out by giving tests and non-tests to students. The test conducted was a written test in the form of a description of 10 questions covering indicators of CTA. The non-test was conducted by giving a student learning independence questionnaire with as many as 15 statements, including five indicators of learning independence. This quantitative research data analysis uses the Rash modeling application with the help of Ministep software. The analysis results show that the learning independence of male and female students in the four junior high schools obtained a percentage of 77.38% in the “good” category. Each indicator of learning independence accepts a percentage above 70%, which is in the excellent category. Meanwhile, the CTA of male and female students from the four junior high schools obtained 75.28% in the “good” category. Each indicator of CTA also gets a percentage of more than 70%, meaning that each indicator is in a good category.

Reflective practices have been recognized as a predictor of professional development because they favor teaching changes that improve the students’ learning. The expressions reflection, practice, and reflective professionals are very present in training programs, but with a diversity of meanings and interpretations. The concept of reflection is linked to professional development and teaching identity. The goal of training reflective teachers is shared on an international level, however, the educational conditions that favor a positive attitude toward reflection have not been sufficiently researched. This article aims to describe the obstacles to a positive attitude toward reflection in pedagogy students according to their teachers. This study is qualitative with an interpretive approach for which an instrumental case study was conducted with 15 university teachers in six Chilean regions.  The results show that both inter-institutional conditions negatively affect attitudes, as well as the lack of models of reflective practice, insufficient teaching, the way teacher reflection is evaluated, and the barriers to reflective practice in schools. The results indicate the need to intentionally teach pedagogical reflection practices and help to recognize its benefits for teaching.

Implementing online learning has led to several issues, especially those related on assessments to measure students’ learning achievement. This study aimed to obtain accurate information on learning assessments for vocational high school (VHS) students during online learning, including assessment for learning (AfL), assessment as learning (AaL), and assessment of learning (AoL). It also investigated students’ perceptions of the assessments based on their grades. This quantitative research employed the survey method, collecting data through questionnaires. The population of this research is VHS students in Indonesia, totaling 86,885 students. The participants of this study were 487 VHS students. The data were analyzed using descriptive and ANOVA techniques. The results show that most VHS students positively perceive the assessment of learning achievements in online learning for AfL, AaL, and AoL aspects. Moreover, there is a significant difference in students' perceptions of the assessment in online learning based on grades. The perception of class XII students is the highest (average value = 3.90) of all classes, while the other classes have an average value of 3.38 for class XI, and the average value of class X is 3.81.

This study aims to analyse the relationship between critical thinking and the learning experience provided by instructors through active learning models, specifically Project-based Learning (PjBL) and Simulation-based Learning (SBL), to the potential achievement of academic performance in undergraduate students. The main analysis technique employed in this research was logistic regression, with additional analysis techniques including discriminant validity, EFA, as well as Kendall’s and Spearman’s correlation, serving as a robustness check. The results of this study indicate significant correlations and effects of critical thinking (CT) on academic performance. Higher levels of CT are associated with a greater likelihood of achieving academic excellence, as indicated by the cum laude distinction, compared to not attaining this distinction. Experiences of receiving PjBL (0.025; 6.816) and SBL (0.014; 14.35) predicted the potential for improving academic performance to reach cum laude recognition, relative to not achieving this distinction. Furthermore, other intercept factors need to be considered to achieve cum laude compared to not achieving cum laude. We recommend that policymakers in higher education, instructors, and others focus on enhancing critical thinking and utilizing both Pub and SBL as learning models to improve students’ academic performance.

This paper presents the meaning and characteristics of collaboration between school counsellors, school principals, and teachers in the context of the COVID-19 pandemic in Slovenia and the extraordinary situation in which work in educational institutions changed dramatically overnight and the community of students and professionals moved into a virtual space. In the first part of the paper, we highlight that a strong network of professionals in an educational institution is key to achieving the vision, goals and quality of educational work. In the second part of the paper, we present the results of a survey conducted through an online questionnaire among 328 Slovenian counsellors during the first wave of COVID-19 in April 2020. The results of this survey show a positive attitude of counsellors towards collaboration with principals and teachers. The emergency situation has raised awareness among all school professionals about the importance of mutual support, while providing an opportunity to reflect on ways to improve mutual collaboration and build mutual relationships that enable quality pedagogical work. One of the biggest challenges for any school community now is to maintain the sense of alliance and mutual support that was created in many schools during the pandemic.

This study aimed to assess the geometric knowledge of student teachers from a university in the Eastern Cape province of South Africa. The study used a sample of 225 first-year student teachers who completed school mathematics baseline assessments on a computer- aided mathematics instruction (CAMI) software. The study adopted a descriptive cross-sectional research design, using quantitative data to measure student teachers’ geometry achievement level, and qualitative data to explain the challenges encountered. The results show that student teachers exhibited a low level of understanding of school-level geometry. The low achievement levels were linked to various factors, such as insufficient grasp of geometry concepts in their secondary school education, difficulty in remembering what was done years ago, low self-confidence, and lack of Information and Communications Technology (ICT) skills along with the limited time for the baseline tests. These results suggest that appropriate measures should be taken to ensure that student teachers acquire the necessary subject-matter knowledge to teach effectively in their future classrooms.

Teaching is a demanding and complex exercise, exposed to the direct or immediate resolution of multiple problematic situations, whether pedagogical, relational, or socio-affective. The teacher's personal resources are often insufficient to cope with the profession's demands. The research reports that there is a gap between research and educational practice. Hence, the objective of this research was to analyze the criteria used by early childhood educators to attribute validity to the written sources of information that guide their pedagogical decisions. The present study follows a qualitative research methodology. The sample for this study was non-probabilistic and consisted of 18 early childhood educators who participated through semi-structured interviews and discussion groups. The data obtained were analyzed by inductive categorization using NVivo 14. The findings revealed that the validity criteria assigned by the educators about the sources of information related to theoretical aspects is mainly attributed to the texts and authors they know, while those referring to practical aspects are attributed to their own experiences or the other educators at the same level. The results showed that specific information and obtaining it in the shortest possible time were the criteria that determined the use of information sources.

This qualitative study investigates the strategies employed by Vietnamese tertiary-level English as a Foreign Language (EFL) teachers to promote learner autonomy (LA) and enhance cultural awareness. This research provides a deeper understanding of EFL teaching practices in this setting, conducted in the context of Vietnam’s evolving educational landscape, where English proficiency and cultural competence are increasingly prioritized. The study utilized semi-structured interviews with nine EFL teachers from two different Vietnamese tertiary institutions, representing various career stages: novice, mid-career, and near-end career. Thematic analysis was employed to analyze the data, revealing a range of strategies encompassing collaborative learning, technology integration, personalized feedback, real-life scenarios and role-play, reflective learning practices, local culture incorporation, contextualized language instruction, critical thinking, and cultural analysis, student-centered environments, interdisciplinary approaches, language skills for intercultural communication, and authentic material use. Findings highlight the multifaceted nature of language teaching, emphasizing not just linguistic competence but also cultural understanding and LA. These strategies are crucial in a globalized world where intercultural communication is a key skill. The study suggests the need for continuous professional development and policy support for diverse and holistic teaching practices. It offers practical insights for EFL educators, particularly in similar socio-cultural contexts, on integrating various strategies to enhance language skills and cultural awareness.